Time structure and useful muon rates for MICE at RAL Alain Blondel, Rob Edgecock

1. Time structure and useful muon rates for MICE at RAL Alain Blondel, Rob Edgecock • UPDATED version with ISIS cycle length = 2 ms • 2. ORIGINAL VERSION with ISIS cycle assumed to be 100 microseconds long

2. Time structure and useful muon rates for MICE at RAL Alain Blondel, Rob Edgecock UPDATED VERSION the time structure of the envisaged MICE running modeat RAL is determined by several elements. .. The repetition rate of ISIS, which is 50 Hz. .. Each time ISIS is cycled, the target is inserted in the ISIS ring during the ISIS flat-top which has a duration of .. During these 2 milliseconds , the beam is hit by the target and pions and muons are produced. .. The proton beam is constituted of 2 bunches of 100 ns length pushed by an RF system operating at 3.1 MHz, i.e. of period 320 nanoseconds. 1 cycle ~6000 bunches ~2 ms

3. How many cycles can we take? UPDATED VERSION This gives a total number of 6000X50= 300 000 bunches per second. Let us assume that an adequate rate is of about 1 muon per bunch reaching the first TOF of MICE. 6000 muons per ISIS cycle The reduction factors calculated by P. Janot were: within the acceptance after the two diffusing plates situated at the first TOF and 10 meters downstream; 1/4 of the muons 6000 / 4 = 1500 muons per ISIS cycle in phase with the RF and are accelerated on crest: 1/6 of the muons This leads to a number of good muons of : 1500 / 6 = 250 muons per ISIS cycle. MICE would then be cooling 12500 muons per second, if the RF were pulsed at 50 Hz with a flat top duration of 2ms This is certainly too optimistic, since the refurbished RF power supplies can presumably not run for more than a duty factor of 0.001, imposing operation of the RF for 1 ms every second. R. Garoby quoted a rise time of 150 microseconds, to which one should add a flat top of 850 microseconds to run at 1 Hz. WE HAVE TO RUN AT 1 CYCLES PER SECOND --- because of RF POWER GOOD MUONS = 250 X 850/2000 = 100 per second

4. RATES UPDATED VERSION Mice will cool around 100 muons per second, providing a measurement of cooling with a statistical precision of 1% for 1000 good muons, taken in 10 seconds, 10-3 in1000 seconds, i.e. less than half an hour. eout /ein = 0.904  0.001 for 9.6% of cooling. Nevertheless, the rate of events to be treated will certainly be much higher. The muons that are not on the crest of the RF wave will certainly be kept, and a fraction of the ‘lost muons’ will have to be measured at least in the upstream tracking device. Furthermore it might be interesting for calibration purposes to run MICE also when the RF is not pulsed. Assuming running at a total of 2Hz (half of the data with the RF off) one still needs to envisage a total rate of around 6000 particles to be reconstructed per second, with a rather large uncertainty due to possible beam related backgrounds, and the efficiency of the emittance generation devices for MICE.

5. Time structure and useful muon rates for MICE at RAL Alain Blondel, Rob Edgecock the time structure of the envisaged MICE running modeat RAL is determined by several elements. .. The repetition rate of ISIS, which is 50 Hz. .. Each time ISIS is cycled, the target is inserted in the ISIS ring during the ISIS flat-top which has a duration of 100 microseconds. .. During these 100 microseconds, the beam is hit by the target and pions and muons are produced. .. The proton beam is constituted of 2 bunches of 100 ns length pushed by an RF system operating at 3.1 MHz, i.e. of period 320 nanoseconds.

6. How many cycles can we take? This gives a total number of 300X50= 15 000 bunches per second. Let us assume that an adequate rate is of about 1 muon per bunch reaching the first TOF of MICE. 300 muons per ISIS cycle The reduction factors calculated by P. Janot were: within the acceptance after the two diffusing plates situated at the first TOF and 10 meters downstream; 1/4 of the muons 300 / 4 = 75 muons per ISIS cycle in phase with the RF and are accelerated on crest: 1/6 of the muons This leads to a number of good muons of : 75 / 6 = 12 muons per ISIS cycle. MICE would then be cooling 600 muons per second, if the RF were pulsed at 50 Hz with a flat top duration of 100 ms. This is certainly too optimistic, since the refurbished RF power supplies can presumably not run for more than a duty factor of 0.001, imposing operation of the RF for 1 ms every second. R. Garoby quoted a rise time of 150 microseconds, to which one should add a flat top of 100 microseconds to match the beam structure. This gives a total pulse length of 250 microseconds, and a RF pulsing rate of 4 Hz. WE CAN HOPE FOR 4 CYCLES PER SECOND --- because of RF POWER GOOD MUONS = 4 X 12 = 48 per second

7. RATES Mice will cool around 12 X 4 = 48 muons per second, providing a measurement of cooling with a statistical precision of 1% for 1000 good muons, taken in 25 seconds, 10-3 in 2500 seconds, i.e. less than an hour. eout /ein = 0.904  0.001 for 9.6% of cooling. Nevertheless, the rate of events to be treated will certainly be much higher. The muons that are not on the crest of the RF wave will certainly be kept, and a fraction of the ‘lost muons’ will have to be measured at least in the upstream tracking device. Furthermore it might be interesting for calibration purposes to run MICE also when the RF is not pulsed. Assuming running at a total of 8 Hz (half of the data with the RF off) one still needs to envisage a total rate of around 3000 particles to be reconstructed per second, with a rather large uncertainty due to possible beam related backgrounds, and the efficiency of the emittance generation devices for MICE.